diff --git a/lib/Quox/Typing/Context.idr b/lib/Quox/Typing/Context.idr
index 7a54387..d231694 100644
--- a/lib/Quox/Typing/Context.idr
+++ b/lib/Quox/Typing/Context.idr
@@ -21,10 +21,6 @@ record LocalVar d n where
   term : Maybe (Term d n) -- if from a `let`
 %runElab deriveIndexed "LocalVar" [Show]
 
-export
-CanShift (LocalVar d) where
-  l // by = {type $= (// by), term $= map (// by)} l
-
 namespace LocalVar
   export %inline
   letVar : (type, term : Term d n) -> LocalVar d n
@@ -34,15 +30,25 @@ namespace LocalVar
   lamVar : (type : Term d n) -> LocalVar d n
   lamVar type = MkLocal {type, term = Nothing}
 
-  subD : DSubst d1 d2 -> LocalVar d1 n -> LocalVar d2 n
-  subD th = {type $= (// th), term $= map (// th)}
+  export %inline
+  mapVar : (Term d n -> Term d' n') -> LocalVar d n -> LocalVar d' n'
+  mapVar f = {type $= f, term $= map f}
 
+  export %inline
+  subD : DSubst d1 d2 -> LocalVar d1 n -> LocalVar d2 n
+  subD th = mapVar (// th)
+
+  export %inline
   weakD : LocalVar d n -> LocalVar (S d) n
   weakD = subD $ shift 1
 
+export %inline CanShift  (LocalVar d) where l // by = mapVar (// by) l
+export %inline CanDSubst LocalVar     where l // by = mapVar (// by) l
+export %inline CanTSubst LocalVar     where l // by = mapVar (// by) l
+
 public export
 TContext : TermLike
-TContext d = Context (\n => LocalVar d n)
+TContext d = Context (LocalVar d)
 
 public export
 QOutput : Nat -> Type
@@ -59,7 +65,7 @@ record TyContext d n where
   {auto dimLen  : Singleton d}
   {auto termLen : Singleton n}
   dctx   : DimEq d
-  dnames : BContext d
+  dnames : BContext d -- only used for printing
   tctx   : TContext d n
   tnames : BContext n -- only used for printing
   qtys   : QContext n -- only used for printing
@@ -122,8 +128,9 @@ CtxExtensionLet0 d = Telescope ((BindName,) . LocalVar d)
 namespace TyContext
   public export %inline
   empty : TyContext 0 0
-  empty =
-    MkTyContext {dctx = new, dnames = [<], tctx = [<], tnames = [<], qtys = [<]}
+  empty = MkTyContext {
+    dctx = new, dnames = [<], tctx = [<], tnames = [<], qtys = [<]
+  }
 
   public export %inline
   null : TyContext d n -> Bool